Déformations équivariantes des courbes stables I : Étude cohomologique

2003/10/09 by Sylvain Maugeais, Maugeais, Sylvain
Mathematics · #14H30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:14H30

paper · pdf · doi:10.48550/arxiv.math/0310137

31 pages, french

arxiv created 2003/10/09 · arxiv updated 2009/12/01

Abstract

Let k be a field, C→ \Spec k be a stable curve and let G be a finite group acting faithfully on the curve C→ \Spec k. In this article, we compute the vector space \Ext¹_G(Ω_C/k, Ø_C), the sheaf Ω_C/k being the sheaf of relative differentials. This vector space is naturally isomorphic to the set of first order G-equivariant deformations of C. The computation we do here will be used in a future article.

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